Algebraic geometry | Algebraic topology

Cyclic cover

In algebraic topology and algebraic geometry, a cyclic cover or cyclic covering is a covering space for which the set of covering transformations forms a cyclic group. As with cyclic groups, there may be both finite and infinite cyclic covers. Cyclic covers have proven useful in the descriptions of knot topology and the algebraic geometry of Calabi–Yau manifolds. In classical algebraic geometry, cyclic covers are a tool used to create new objects from existing ones through, for example, a field extension by a root element. The powers of the root element form a cyclic group and provide the basis for a cyclic cover. A line bundle over a complex projective variety with torsion index may induce a cyclic Galois covering with cyclic group of order . (Wikipedia).

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Cyclic Groups, Generators, and Cyclic Subgroups | Abstract Algebra

We introduce cyclic groups, generators of cyclic groups, and cyclic subgroups. We discuss an isomorphism from finite cyclic groups to the integers mod n, as well as an isomorphism from infinite cyclic groups to the integers. We establish a cyclic group of order n is isomorphic to Zn, and a

From playlist Abstract Algebra

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Cyclic Quadrilateral: Proof Hint!

Link: https://www.geogebra.org/m/KYdypjws

From playlist Geometry: Dynamic Interactives!

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Cyclic Groups (Abstract Algebra)

Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. Be sure to subscribe s

From playlist Abstract Algebra

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Abstract Algebra | Subgroups of Cyclic Groups

We prove that all subgroups of cyclic groups are themselves cyclic. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Cyclic Quadrilaterals and Parallel Lines in Circles

Watch more videos on http://www.brightstorm.com/math/geometry SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► https

From playlist Geometry

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Definition of a Cyclic Group with Examples

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Cyclic Group with Examples

From playlist Abstract Algebra

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Abstract Algebra | Cyclic Subgroups

We define the notion of a cyclic subgroup and give a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Lecture 14: The Definition of TC

In this video, we finally give the definition of topological cyclic homology. In fact, we will give two definitions: the first is abstract in terms of a mapping spectrum spectrum in cyclotomic spectra and then we unfold this to a concrete definition on terms of negative topological cyclic

From playlist Topological Cyclic Homology

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Lead Mining Safety

Find out how lead miners counteract some of their hazardous working conditions in this clip from Discovery Channel's "HowStuffWorks" show.

From playlist HowStuffWorks TV Show

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Kirk McDermott: Topological Aspects of the Shift Dynamics of the Groups of Fibonacci Type

Kirk McDermott, Slippery Rock University of Pennsylvania Title: Topological Aspects of the Shift Dynamics of the Groups of Fibonacci Type A group is cyclically presented if it admits a presentation with a certain cyclic symmetry. Such a symmetry induces a periodic automorphism of the group

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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Taut foliations and cyclic branched covers - Cameron Gordon

Cameron Gordon, Univ Texas Workshop on Flows, Foliations and Contact Structures 2015-2016 Monday, December 7, 2015 - 08:00 to Friday, December 11, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 aca

From playlist Workshop on Flows, Foliations and Contact Structures

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Colouring Tournaments - Paul Seymour

Paul Seymour Princeton University December 13, 2010 A ``tournament'' is a digraph obtained from a complete graph by directing its edges, and ``colouring'' a tournament means partitioning its vertex set into acyclic subsets (``acyclic'' means the subdigraph induced on the subset has no dire

From playlist Mathematics

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CTNT 2020 - Stacky curves in characteristic p - Andrew Kobin

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Conference Videos

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Markus Pflaum: The transverse index theorem for proper cocompact actions of Lie groupoids

The talk is based on joint work with H. Posthuma and X. Tang. We consider a proper cocompact action of a Lie groupoid and define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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Derived categories of cyclic covers and their branch divisors - Alexander Perry

Alexander Perry Harvard University April 29, 2015 Given a variety YY with a rectangular Lefschetz decomposition of its derived category, I will discuss an interesting relation between the derived categories of a cyclic cover of YY and its branch divisor. As examples, I will describe the c

From playlist Mathematics

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11 Data Analytics: Variogram Interpretation

Lecture on variogram interpretation.

From playlist Data Analytics and Geostatistics

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Emily Stark: The visual boundary of hyperbolic free-by-cyclic groups

Abstract: Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, th

From playlist Topology

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Direct Products of Finite Cyclic Groups Video 1

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Direct Products of Finite Cyclic Groups Video 1. How to determine if a direct product of finite cyclic groups is itself cyclic. This video has very easy examples.

From playlist Abstract Algebra

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Cross Products Using Levi Civita Symbol

Everyone has their favorite method of calculating cross products. Today I go over the way I was taught, and then a more formal way of doing cross products by using the levi civita tensor.

From playlist Math/Derivation Videos

Related pages

Knot (mathematics) | Field extension | Covering space | Torsion tensor | Line bundle | Projective variety | Algebraic geometry | Cyclic group | Calabi–Yau manifold | Algebraic topology